Question

a. Graph the line that passes through the point (4, 3) and has a y-intercept at (0,-1)b. What is the x -intercept of this line?

Answer 1

To obtain the slope of a line given two points, use the formula below

`m=(y_2-y_1)/(x_2-x_1)`

In our case,

`m=(3-(-1))/(4-0)=(4)/(4)=1`

Then, in general, the slope-intercept form of the equation of a line is

`\begin{gathered} y=mx+b \\ m\rightarrow\text{ slope} \\ b\rightarrow\text{ y-intercept} \end{gathered}`

Thus, in our case,

`\begin{gathered} \Rightarrow y=1*x+(-1)=x-1 \\ \Rightarrow y=x-1 \end{gathered}`

a) The equation of the line is y=x-1. To graph it, draw (4,3) and (0,-1) on the plane; then, cross them using a line, as shown below

b) Set y=0 in the equation we found in part a); then, solve for x, as shown below

`\begin{gathered} y=0 \\ \Rightarrow0=x-1 \\ \Rightarrow x=1 \\ \Rightarrow(1,0) \end{gathered}`

The x-intercept of the line is (1,0)